Noémie Combe
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig
Germany

Office: F3 11

Contact:
   Email

   Phone:
+49 341 9959 775

   Fax:
+49 341 9959 658

Noemie Combe

Research interests

  • My research is in the field of mathematics, specifically at the intersection of algebraic geometry and algebraic topology. I study objects such as moduli spaces of genus g curves with marked points, operads (a type of algebra), Frobenius manifolds and Grothendieck–Teichmüller groups. I am also interested in Koszulness problems. 

I also work with real/complex algebraic varieties. In particular, I am interested in counting the number of connected components of a real algebraic variety of a fixed degree. 

 

  • PhD Thesis. 

I did my PhD thesis at the University of Aix-Marseille and Sorbonne University (Université Paris 6).

Title: Une nouvelle decomposition de l'espace des polynômes à racines simples: application à la cohomologie des groupes de tresses.

Supervisors: Bernard Coupet & Norbert A'Campo.

 

Description:

This Thesis gives a new approach to compute cohomology groups of configuration spaces of points in the complex plane. The approach relies on introducing a Čech cover of this space, where each stratum is indexed by a Gauss drawing (colored graph embedded in the complex plane). 

 

  • Master Thesis. 

I did my master thesis at the University of Geneva (Switzerland) with Daniel Coray. The title is Étude de la connexité des surfaces algébriques réelles.

In this Thesis, I contributed to the problem of counting the number of connected components of real algebraic varieties of a given degree (which is a problem deeply related to the Hilbert 16th problem). In particular, I showed that a degree 4 algebraic surface, invariant under the octahedral group, has a maximal number of connected components equal to 9. 

Publications

Accepted publications

  • 2007. N. C. Combe, Solution d’un problème de géomètrie euclidienne, Tangente Sup 39–40, p.30 Ed. Pole Paris.
  • 2018. N. C. Combe, Geometric classification of real ternary octahedral quartics, Discrete and Computational Geometry, 60 Issue 2.
  • 2018. N. C. Combe, On Coxeter algebraic varieties: the geometry of CBn quartics, Math. Semesterberichte, vol 66 Issue 1.
  • 2018. N. C. Combe, Métamorphoses de dessins de polynômes complexes, Chapter from, L’espace des transformations. Editeur Baudouin Janninck (presses du réel)
  • 2018. N. C. Combe, Toucher le mystère de l’univers, Wzsystko co najwazniejsze, For Marie Curie’s bicentenary.
  • 2018. N. C. Combe, Doktnac tajemnicy swiata, Wzsystko co najwazniejsze, For Marie Curie’s bicentenary.
  • 2019. N. C. Combe, Y. I. Manin, Symmetries of genus zero modular operad,  publications of the AMS, Dubrovin's Memorial.
  • 2020 N. C. Combe, Y. I. Manin, F-manifolds and geometry of information, accepted in BLMS 

 

Monographs

  • 2016. N. C. Combe, Étude de la connexité des surfaces algébriques réelles, Éditions Universitaires Européennes.

Preprints 

  • 2018. N. C. Combe, Čech cover of the complement of the discriminant variety, Arxiv:1808.08411.  
  • 2018. N. C. Combe, Geometric invariants of the configuration space of d marked points on the complex plane, ArXiv:1808.08411. 

  • 2019. N. C. Combe, Y. I. Manin, Genus zero modular operad and absolute Galois group, Arxiv:1907.10313.

  • 2019. N. C. Combe, Gauss Skizze-Operad and monodromy on semisimple Frobenius manifolds, MPIM 45-19 preprints.

 

Ongoing work

  • Universal operadic deformation group, with Ricardo Campos and Bruno Vallette

Collaborations

Working group about operads and related topics, with Joscha Diehl. 

To start on 25/03

 

Workshop : Operads and Koszul duality 19 Oct - 23 Oc, co-organized with Geoffroy Horel. 

 

 

Personal homepage

Curriculum vitae

Current position

I am a Minerva Fast Track Fellow at the Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany).

 

Previous positions 

  • 09/2018 – 12/2019:  post-doc at the Max-Planck Institute for Mathematics in Bonn, in Germany, where I worked with Yuri I. Manin. 
  • 09/2017 – 08/2019:  visiting assistant Professor, at  Sorbonne University (Paris 6).
  • 09/2013 – 08/2017:  monitorat and PhD - Teaching assistant - Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, Marseille.

 

Education

  • 2013 - 2016: PhD excellence Labex grant. Supervision by Bernard Coupet and Norbert A'Campo, Aix--Marseille University and Sorbonne University.             
  • 2012 - 2013: Master in pure mathematics, direction: research. University of Geneva (Switzerland). Supervisor of Master thesis: Daniel Coray
  • 2009 - 2012: Bachelor in pure mathematics, University of Geneva (Switzerland). Supervisor of Bachelor thesis: Stanislas Smirnov.
  • 2008 - 2009:  Classes preparatoires (CMS)​​​​​​,​ EPFL (Ecole Polytechnique Fédérale  de Lausanne), Switzerland.

 

 

20.10.2020, 14:21